The present invention can provide a distinctive method and process for making polymer fibers (62) and nonwoven fabric webs (60). The method can include providing a fiber material that exhibits a low crystallization rate. In a particular aspect, the fiber material can be subjected to an anneal-quench at an anneal-quench temperature that approximates a prime-temperature at which the polymer material most rapidly crystallizes. In another aspect, the fiber material can be subjected to a fiber-draw at a selected fiber-draw temperature, and in a further aspect, the fiber-draw temperature can be configured to approximate the prime-temperature of the polymer material. In still other aspects, the fiber material can be subjected to a relatively small amount of fiber-draw, and the fiber-draw can be provided at a relatively low fiber-draw speed.